LMFDB - Embedded newform 234.5.i.b.109.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,5,Mod(73,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.73"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	234.i (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,12,0,0,-18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1885713616$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 234x^{4} + 13689x^{2} + 60516 $ x^6 + 234x^4 + 13689x^2 + 60516
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.3
Root			$-2.19267i$ of defining polynomial
Character	$\chi$	$=$	234.109
Dual form			234.5.i.b.73.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 2.00000i) q^{2} -8.00000i q^{4} +(28.1144 - 28.1144i) q^{5} +(-49.0778 - 49.0778i) q^{7} +(-16.0000 - 16.0000i) q^{8} -112.458i q^{10} +(-125.843 - 125.843i) q^{11} +(76.8118 + 150.536i) q^{13} -196.311 q^{14} -64.0000 q^{16} +293.870i q^{17} +(-165.724 + 165.724i) q^{19} +(-224.916 - 224.916i) q^{20} -503.372 q^{22} -297.165i q^{23} -955.844i q^{25} +(454.695 + 147.448i) q^{26} +(-392.622 + 392.622i) q^{28} +1060.76 q^{29} +(-511.960 + 511.960i) q^{31} +(-128.000 + 128.000i) q^{32} +(587.740 + 587.740i) q^{34} -2759.59 q^{35} +(-292.878 - 292.878i) q^{37} +662.895i q^{38} -899.662 q^{40} +(804.161 - 804.161i) q^{41} -1005.69i q^{43} +(-1006.74 + 1006.74i) q^{44} +(-594.330 - 594.330i) q^{46} +(-1325.64 - 1325.64i) q^{47} +2416.26i q^{49} +(-1911.69 - 1911.69i) q^{50} +(1204.28 - 614.494i) q^{52} -574.799 q^{53} -7076.02 q^{55} +1570.49i q^{56} +(2121.52 - 2121.52i) q^{58} +(-2237.69 - 2237.69i) q^{59} -6068.83 q^{61} +2047.84i q^{62} +512.000i q^{64} +(6391.74 + 2072.70i) q^{65} +(3155.98 - 3155.98i) q^{67} +2350.96 q^{68} +(-5519.18 + 5519.18i) q^{70} +(1607.78 - 1607.78i) q^{71} +(22.6121 + 22.6121i) q^{73} -1171.51 q^{74} +(1325.79 + 1325.79i) q^{76} +12352.2i q^{77} +6576.52 q^{79} +(-1799.32 + 1799.32i) q^{80} -3216.64i q^{82} +(5691.45 - 5691.45i) q^{83} +(8261.99 + 8261.99i) q^{85} +(-2011.39 - 2011.39i) q^{86} +4026.98i q^{88} +(-4243.56 - 4243.56i) q^{89} +(3618.20 - 11157.7i) q^{91} -2377.32 q^{92} -5302.58 q^{94} +9318.47i q^{95} +(3532.64 - 3532.64i) q^{97} +(4832.51 + 4832.51i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 18 q^{5} - 42 q^{7} - 96 q^{8} + 18 q^{11} + 90 q^{13} - 168 q^{14} - 384 q^{16} - 366 q^{19} + 144 q^{20} + 72 q^{22} - 12 q^{26} - 336 q^{28} + 6228 q^{29} + 402 q^{31} - 768 q^{32} + 1944 q^{34}+ \cdots + 17076 q^{98}+O(q^{100}) $ 6 * q + 12 * q^2 - 18 * q^5 - 42 * q^7 - 96 * q^8 + 18 * q^11 + 90 * q^13 - 168 * q^14 - 384 * q^16 - 366 * q^19 + 144 * q^20 + 72 * q^22 - 12 * q^26 - 336 * q^28 + 6228 * q^29 + 402 * q^31 - 768 * q^32 + 1944 * q^34 - 3024 * q^35 + 5298 * q^37 + 576 * q^40 + 2430 * q^41 + 144 * q^44 - 1872 * q^46 - 4014 * q^47 - 7908 * q^50 - 768 * q^52 - 6516 * q^53 - 28764 * q^55 + 12456 * q^58 - 7434 * q^59 + 7164 * q^61 + 14598 * q^65 + 5790 * q^67 + 7776 * q^68 - 6048 * q^70 - 15246 * q^71 - 4254 * q^73 + 21192 * q^74 + 2928 * q^76 + 23364 * q^79 + 1152 * q^80 + 38034 * q^83 + 30672 * q^85 - 11160 * q^86 - 4122 * q^89 - 11922 * q^91 - 7488 * q^92 - 16056 * q^94 - 1362 * q^97 + 17076 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	8.00000i		−	0.500000i
$5$	28.1144	−	28.1144i	1.12458	−	1.12458i	0.133534	−	0.991044i	$-0.457368\pi$
$5$	28.1144	−	28.1144i	1.12458	−	1.12458i	0.991044	−	0.133534i	$-0.0426324\pi$
$6$		0			0
$7$	−49.0778	−	49.0778i	−1.00159	−	1.00159i	−0.999999	−	0.00158846i	$-0.999494\pi$
$7$	−49.0778	−	49.0778i	−1.00159	−	1.00159i	−0.00158846	−	0.999999i	$-0.500506\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$		0			0
$10$		−	112.458i		−	1.12458i
$11$	−125.843	−	125.843i	−1.04003	−	1.04003i	−0.999165	−	0.0408609i	$-0.986990\pi$
$11$	−125.843	−	125.843i	−1.04003	−	1.04003i	−0.0408609	−	0.999165i	$-0.513010\pi$
$12$		0			0
$13$	76.8118	+	150.536i	0.454507	+	0.890743i
$13$	76.8118	+	150.536i	0.454507	+	0.890743i
$14$	−196.311			−1.00159
$15$		0			0
$16$	−64.0000			−0.250000
$17$			293.870i			1.01685i	0.861106	+	0.508426i	$0.169772\pi$
$17$			293.870i			1.01685i	−0.861106	+	0.508426i	$0.830228\pi$
$18$		0			0
$19$	−165.724	+	165.724i	−0.459069	+	0.459069i	−0.898350	−	0.439281i	$-0.855233\pi$
$19$	−165.724	+	165.724i	−0.459069	+	0.459069i	0.439281	+	0.898350i	$0.355233\pi$
$20$	−224.916	−	224.916i	−0.562289	−	0.562289i
$21$		0			0
$22$	−503.372			−1.04003
$23$		−	297.165i		−	0.561748i	−0.959745	−	0.280874i	$-0.909376\pi$
$23$		−	297.165i		−	0.561748i	0.959745	−	0.280874i	$-0.0906244\pi$
$24$		0			0
$25$		−	955.844i		−	1.52935i
$26$	454.695	+	147.448i	0.672625	+	0.218118i
$27$		0			0
$28$	−392.622	+	392.622i	−0.500794	+	0.500794i
$29$	1060.76			1.26131			0.630655	−	0.776064i	$-0.282787\pi$
$29$	1060.76			1.26131			0.630655	+	0.776064i	$0.282787\pi$
$30$		0			0
$31$	−511.960	+	511.960i	−0.532736	+	0.532736i	−0.921386	−	0.388649i	$-0.872942\pi$
$31$	−511.960	+	511.960i	−0.532736	+	0.532736i	0.388649	+	0.921386i	$0.372942\pi$
$32$	−128.000	+	128.000i	−0.125000	+	0.125000i
$33$		0			0
$34$	587.740	+	587.740i	0.508426	+	0.508426i
$35$	−2759.59			−2.25273
$36$		0			0
$37$	−292.878	−	292.878i	−0.213936	−	0.213936i	0.592001	−	0.805937i	$-0.298338\pi$
$37$	−292.878	−	292.878i	−0.213936	−	0.213936i	−0.805937	+	0.592001i	$0.798338\pi$
$38$			662.895i			0.459069i
$39$		0			0
$40$	−899.662			−0.562289
$41$	804.161	−	804.161i	0.478383	−	0.478383i	−0.426232	−	0.904614i	$-0.640159\pi$
$41$	804.161	−	804.161i	0.478383	−	0.478383i	0.904614	+	0.426232i	$0.140159\pi$
$42$		0			0
$43$		−	1005.69i		−	0.543913i	−0.962310	−	0.271956i	$-0.912329\pi$
$43$		−	1005.69i		−	0.543913i	0.962310	−	0.271956i	$-0.0876707\pi$
$44$	−1006.74	+	1006.74i	−0.520013	+	0.520013i
$45$		0			0
$46$	−594.330	−	594.330i	−0.280874	−	0.280874i
$47$	−1325.64	−	1325.64i	−0.600111	−	0.600111i	0.340231	−	0.940342i	$-0.389495\pi$
$47$	−1325.64	−	1325.64i	−0.600111	−	0.600111i	−0.940342	+	0.340231i	$0.889495\pi$
$48$		0			0
$49$			2416.26i			1.00635i
$50$	−1911.69	−	1911.69i	−0.764675	−	0.764675i
$51$		0			0
$52$	1204.28	−	614.494i	0.445371	−	0.227254i
$53$	−574.799			−0.204628			−0.102314	−	0.994752i	$-0.532625\pi$
$53$	−574.799			−0.204628			−0.102314	+	0.994752i	$0.532625\pi$
$54$		0			0
$55$	−7076.02			−2.33918
$56$			1570.49i			0.500794i
$57$		0			0
$58$	2121.52	−	2121.52i	0.630655	−	0.630655i
$59$	−2237.69	−	2237.69i	−0.642829	−	0.642829i	0.308421	−	0.951250i	$-0.400200\pi$
$59$	−2237.69	−	2237.69i	−0.642829	−	0.642829i	−0.951250	+	0.308421i	$0.900200\pi$
$60$		0			0
$61$	−6068.83			−1.63097			−0.815484	−	0.578779i	$-0.803529\pi$
$61$	−6068.83			−1.63097			−0.815484	+	0.578779i	$0.803529\pi$
$62$			2047.84i			0.532736i
$63$		0			0
$64$			512.000i			0.125000i
$65$	6391.74	+	2072.70i	1.51284	+	0.490581i
$66$		0			0
$67$	3155.98	−	3155.98i	0.703046	−	0.703046i	−0.262017	−	0.965063i	$-0.584388\pi$
$67$	3155.98	−	3155.98i	0.703046	−	0.703046i	0.965063	+	0.262017i	$0.0843876\pi$
$68$	2350.96			0.508426
$69$		0			0
$70$	−5519.18	+	5519.18i	−1.12636	+	1.12636i
$71$	1607.78	−	1607.78i	0.318940	−	0.318940i	−0.529420	−	0.848360i	$-0.677590\pi$
$71$	1607.78	−	1607.78i	0.318940	−	0.318940i	0.848360	+	0.529420i	$0.177590\pi$
$72$		0			0
$73$	22.6121	+	22.6121i	0.00424321	+	0.00424321i	0.709225	−	0.704982i	$-0.249045\pi$
$73$	22.6121	+	22.6121i	0.00424321	+	0.00424321i	−0.704982	+	0.709225i	$0.749045\pi$
$74$	−1171.51			−0.213936
$75$		0			0
$76$	1325.79	+	1325.79i	0.229534	+	0.229534i
$77$			12352.2i			2.08335i
$78$		0			0
$79$	6576.52			1.05376			0.526880	−	0.849940i	$-0.323362\pi$
$79$	6576.52			1.05376			0.526880	+	0.849940i	$0.323362\pi$
$80$	−1799.32	+	1799.32i	−0.281144	+	0.281144i
$81$		0			0
$82$		−	3216.64i		−	0.478383i
$83$	5691.45	−	5691.45i	0.826165	−	0.826165i	−0.160819	−	0.986984i	$-0.551414\pi$
$83$	5691.45	−	5691.45i	0.826165	−	0.826165i	0.986984	+	0.160819i	$0.0514136\pi$
$84$		0			0
$85$	8261.99	+	8261.99i	1.14353	+	1.14353i
$86$	−2011.39	−	2011.39i	−0.271956	−	0.271956i
$87$		0			0
$88$			4026.98i			0.520013i
$89$	−4243.56	−	4243.56i	−0.535735	−	0.535735i	0.386538	−	0.922273i	$-0.373671\pi$
$89$	−4243.56	−	4243.56i	−0.535735	−	0.535735i	−0.922273	+	0.386538i	$0.873671\pi$
$90$		0			0
$91$	3618.20	−	11157.7i	0.436928	−	1.34739i
$92$	−2377.32			−0.280874
$93$		0			0
$94$	−5302.58			−0.600111
$95$			9318.47i			1.03252i
$96$		0			0
$97$	3532.64	−	3532.64i	0.375453	−	0.375453i	−0.494006	−	0.869459i	$-0.664468\pi$
$97$	3532.64	−	3532.64i	0.375453	−	0.375453i	0.869459	+	0.494006i	$0.164468\pi$
$98$	4832.51	+	4832.51i	0.503177	+	0.503177i
$99$		0			0
$100$	−7646.75			−0.764675
$101$		−	18045.3i		−	1.76897i	−0.466567	−	0.884486i	$-0.654509\pi$
$101$		−	18045.3i		−	1.76897i	0.466567	−	0.884486i	$-0.345491\pi$
$102$		0			0
$103$			2128.08i			0.200592i	0.994958	+	0.100296i	$0.0319790\pi$
$103$			2128.08i			0.200592i	−0.994958	+	0.100296i	$0.968021\pi$
$104$	1179.58	−	3637.56i	0.109059	−	0.336313i
$105$		0			0
$106$	−1149.60	+	1149.60i	−0.102314	+	0.102314i
$107$	8838.57			0.771995			0.385997	−	0.922500i	$-0.373857\pi$
$107$	8838.57			0.771995			0.385997	+	0.922500i	$0.373857\pi$
$108$		0			0
$109$	−2517.64	+	2517.64i	−0.211905	+	0.211905i	−0.805076	−	0.593171i	$-0.797876\pi$
$109$	−2517.64	+	2517.64i	−0.211905	+	0.211905i	0.593171	+	0.805076i	$0.297876\pi$
$110$	−14152.0	+	14152.0i	−1.16959	+	1.16959i
$111$		0			0
$112$	3140.98	+	3140.98i	0.250397	+	0.250397i
$113$	−1933.19			−0.151397			−0.0756984	−	0.997131i	$-0.524119\pi$
$113$	−1933.19			−0.151397			−0.0756984	+	0.997131i	$0.524119\pi$
$114$		0			0
$115$	−8354.62	−	8354.62i	−0.631730	−	0.631730i
$116$		−	8486.09i		−	0.630655i
$117$		0			0
$118$	−8950.76			−0.642829
$119$	14422.5	−	14422.5i	1.01847	−	1.01847i
$120$		0			0
$121$			17032.0i			1.16331i
$122$	−12137.7	+	12137.7i	−0.815484	+	0.815484i
$123$		0			0
$124$	4095.68	+	4095.68i	0.266368	+	0.266368i
$125$	−9301.50	−	9301.50i	−0.595296	−	0.595296i
$126$		0			0
$127$		−	7762.26i		−	0.481261i	−0.970617	−	0.240630i	$-0.922646\pi$
$127$		−	7762.26i		−	0.481261i	0.970617	−	0.240630i	$-0.0773542\pi$
$128$	1024.00	+	1024.00i	0.0625000	+	0.0625000i
$129$		0			0
$130$	16928.9	−	8638.08i	1.00171	−	0.511129i
$131$	−10467.8			−0.609974			−0.304987	−	0.952357i	$-0.598652\pi$
$131$	−10467.8			−0.609974			−0.304987	+	0.952357i	$0.598652\pi$
$132$		0			0
$133$	16266.7			0.919595
$134$		−	12623.9i		−	0.703046i
$135$		0			0
$136$	4701.92	−	4701.92i	0.254213	−	0.254213i
$137$	10192.9	+	10192.9i	0.543072	+	0.543072i	0.924428	−	0.381356i	$-0.124543\pi$
$137$	10192.9	+	10192.9i	0.543072	+	0.543072i	−0.381356	+	0.924428i	$0.624543\pi$
$138$		0			0
$139$	29697.1			1.53704			0.768519	−	0.639827i	$-0.220994\pi$
$139$	29697.1			1.53704			0.768519	+	0.639827i	$0.220994\pi$
$140$			22076.7i			1.12636i
$141$		0			0
$142$		−	6431.11i		−	0.318940i
$143$	9277.63	−	28610.1i	0.453696	−	1.39910i
$144$		0			0
$145$	29822.7	−	29822.7i	1.41844	−	1.41844i
$146$	90.4483			0.00424321
$147$		0			0
$148$	−2343.02	+	2343.02i	−0.106968	+	0.106968i
$149$	22208.2	−	22208.2i	1.00033	−	1.00033i	0.000326486	−	1.00000i	$-0.499896\pi$
$149$	22208.2	−	22208.2i	1.00033	−	1.00033i	1.00000		0.000326486i	$-0.000103924\pi$
$150$		0			0
$151$	−27423.8	−	27423.8i	−1.20274	−	1.20274i	−0.973328	−	0.229417i	$-0.926318\pi$
$151$	−27423.8	−	27423.8i	−1.20274	−	1.20274i	−0.229417	−	0.973328i	$-0.573682\pi$
$152$	5303.16			0.229534
$153$		0			0
$154$	24704.4	+	24704.4i	1.04168	+	1.04168i
$155$			28786.9i			1.19821i
$156$		0			0
$157$	3402.51			0.138038			0.0690192	−	0.997615i	$-0.478013\pi$
$157$	3402.51			0.138038			0.0690192	+	0.997615i	$0.478013\pi$
$158$	13153.0	−	13153.0i	0.526880	−	0.526880i
$159$		0			0
$160$			7197.30i			0.281144i
$161$	−14584.2	+	14584.2i	−0.562640	+	0.562640i
$162$		0			0
$163$	19832.3	+	19832.3i	0.746445	+	0.746445i	0.973810	−	0.227365i	$-0.0730110\pi$
$163$	19832.3	+	19832.3i	0.746445	+	0.746445i	−0.227365	+	0.973810i	$0.573011\pi$
$164$	−6433.29	−	6433.29i	−0.239191	−	0.239191i
$165$		0			0
$166$		−	22765.8i		−	0.826165i
$167$	6728.75	+	6728.75i	0.241269	+	0.241269i	0.817375	−	0.576106i	$-0.195428\pi$
$167$	6728.75	+	6728.75i	0.241269	+	0.241269i	−0.576106	+	0.817375i	$0.695428\pi$
$168$		0			0
$169$	−16760.9	+	23125.8i	−0.586846	+	0.809699i
$170$	33048.0			1.14353
$171$		0			0
$172$	−8045.56			−0.271956
$173$			32296.9i			1.07912i	0.841948	+	0.539558i	$0.181409\pi$
$173$			32296.9i			1.07912i	−0.841948	+	0.539558i	$0.818591\pi$
$174$		0			0
$175$	−46910.7	+	46910.7i	−1.53178	+	1.53178i
$176$	8053.96	+	8053.96i	0.260006	+	0.260006i
$177$		0			0
$178$	−16974.2			−0.535735
$179$			41174.2i			1.28505i	0.766266	+	0.642524i	$0.222113\pi$
$179$			41174.2i			1.28505i	−0.766266	+	0.642524i	$0.777887\pi$
$180$		0			0
$181$			31653.5i			0.966196i	0.875566	+	0.483098i	$0.160489\pi$
$181$			31653.5i			0.966196i	−0.875566	+	0.483098i	$0.839511\pi$
$182$	−15079.0	−	29551.8i	−0.455229	−	0.892157i
$183$		0			0
$184$	−4754.64	+	4754.64i	−0.140437	+	0.140437i
$185$	−16468.2			−0.481175
$186$		0			0
$187$	36981.5	−	36981.5i	1.05755	−	1.05755i
$188$	−10605.2	+	10605.2i	−0.300055	+	0.300055i
$189$		0			0
$190$	18636.9	+	18636.9i	0.516258	+	0.516258i
$191$	15395.5			0.422013			0.211007	−	0.977485i	$-0.432326\pi$
$191$	15395.5			0.422013			0.211007	+	0.977485i	$0.432326\pi$
$192$		0			0
$193$	−32248.9	−	32248.9i	−0.865765	−	0.865765i	0.126235	−	0.992000i	$-0.459711\pi$
$193$	−32248.9	−	32248.9i	−0.865765	−	0.865765i	−0.992000	+	0.126235i	$0.959711\pi$
$194$		−	14130.6i		−	0.375453i
$195$		0			0
$196$	19330.0			0.503177
$197$	28366.7	−	28366.7i	0.730930	−	0.730930i	−0.239874	−	0.970804i	$-0.577106\pi$
$197$	28366.7	−	28366.7i	0.730930	−	0.730930i	0.970804	+	0.239874i	$0.0771062\pi$
$198$		0			0
$199$			41308.6i			1.04312i	0.853214	+	0.521560i	$0.174650\pi$
$199$			41308.6i			1.04312i	−0.853214	+	0.521560i	$0.825350\pi$
$200$	−15293.5	+	15293.5i	−0.382338	+	0.382338i
$201$		0			0
$202$	−36090.6	−	36090.6i	−0.884486	−	0.884486i
$203$	−52059.8	−	52059.8i	−1.26331	−	1.26331i
$204$		0			0
$205$		−	45217.1i		−	1.07596i
$206$	4256.16	+	4256.16i	0.100296	+	0.100296i
$207$		0			0
$208$	−4915.95	−	9634.28i	−0.113627	−	0.222686i
$209$	41710.4			0.954886
$210$		0			0
$211$	53697.8			1.20612			0.603062	−	0.797695i	$-0.293947\pi$
$211$	53697.8			1.20612			0.603062	+	0.797695i	$0.293947\pi$
$212$			4598.39i			0.102314i
$213$		0			0
$214$	17677.1	−	17677.1i	0.385997	−	0.385997i
$215$	−28274.6	−	28274.6i	−0.611672	−	0.611672i
$216$		0			0
$217$	50251.7			1.06716
$218$			10070.6i			0.211905i
$219$		0			0
$220$			56608.1i			1.16959i
$221$	−44237.9	+	22572.7i	−0.905753	+	0.462167i
$222$		0			0
$223$	−39762.2	+	39762.2i	−0.799578	+	0.799578i	−0.983029	−	0.183451i	$-0.941273\pi$
$223$	−39762.2	+	39762.2i	−0.799578	+	0.799578i	0.183451	+	0.983029i	$0.441273\pi$
$224$	12563.9			0.250397
$225$		0			0
$226$	−3866.37	+	3866.37i	−0.0756984	+	0.0756984i
$227$	13759.5	−	13759.5i	0.267025	−	0.267025i	−0.560876	−	0.827900i	$-0.689535\pi$
$227$	13759.5	−	13759.5i	0.267025	−	0.267025i	0.827900	+	0.560876i	$0.189535\pi$
$228$		0			0
$229$	−26261.1	−	26261.1i	−0.500774	−	0.500774i	0.410905	−	0.911678i	$-0.365213\pi$
$229$	−26261.1	−	26261.1i	−0.500774	−	0.500774i	−0.911678	+	0.410905i	$0.865213\pi$
$230$	−33418.5			−0.631730
$231$		0			0
$232$	−16972.2	−	16972.2i	−0.315327	−	0.315327i
$233$			41383.8i			0.762287i	0.924516	+	0.381144i	$0.124470\pi$
$233$			41383.8i			0.762287i	−0.924516	+	0.381144i	$0.875530\pi$
$234$		0			0
$235$	−74539.5			−1.34974
$236$	−17901.5	+	17901.5i	−0.321415	+	0.321415i
$237$		0			0
$238$		−	57689.9i		−	1.01847i
$239$	−1600.45	+	1600.45i	−0.0280187	+	0.0280187i	−0.720977	−	0.692959i	$-0.756307\pi$
$239$	−1600.45	+	1600.45i	−0.0280187	+	0.0280187i	0.692959	+	0.720977i	$0.256307\pi$
$240$		0			0
$241$	−33028.9	−	33028.9i	−0.568669	−	0.568669i	0.363086	−	0.931755i	$-0.381723\pi$
$241$	−33028.9	−	33028.9i	−0.568669	−	0.568669i	−0.931755	+	0.363086i	$0.881723\pi$
$242$	34064.0	+	34064.0i	0.581654	+	0.581654i
$243$		0			0
$244$			48550.7i			0.815484i
$245$	67931.7	+	67931.7i	1.13172	+	1.13172i
$246$		0			0
$247$	−37676.9	−	12217.8i	−0.617562	−	0.200262i
$248$	16382.7			0.266368
$249$		0			0
$250$	−37206.0			−0.595296
$251$		−	16019.3i		−	0.254271i	−0.991885	−	0.127135i	$-0.959422\pi$
$251$		−	16019.3i		−	0.254271i	0.991885	−	0.127135i	$-0.0405783\pi$
$252$		0			0
$253$	−37396.1	+	37396.1i	−0.584233	+	0.584233i
$254$	−15524.5	−	15524.5i	−0.240630	−	0.240630i
$255$		0			0
$256$	4096.00			0.0625000
$257$		−	51851.4i		−	0.785044i	−0.919743	−	0.392522i	$-0.871603\pi$
$257$		−	51851.4i		−	0.785044i	0.919743	−	0.392522i	$-0.128397\pi$
$258$		0			0
$259$			28747.6i			0.428550i
$260$	16581.6	−	51133.9i	0.245290	−	0.756419i
$261$		0			0
$262$	−20935.5	+	20935.5i	−0.304987	+	0.304987i
$263$	−112584.			−1.62767			−0.813833	−	0.581099i	$-0.802623\pi$
$263$	−112584.			−1.62767			−0.813833	+	0.581099i	$0.802623\pi$
$264$		0			0
$265$	−16160.2	+	16160.2i	−0.230120	+	0.230120i
$266$	32533.4	−	32533.4i	0.459797	−	0.459797i
$267$		0			0
$268$	−25247.8	−	25247.8i	−0.351523	−	0.351523i
$269$	−12549.4			−0.173428			−0.0867139	−	0.996233i	$-0.527637\pi$
$269$	−12549.4			−0.173428			−0.0867139	+	0.996233i	$0.527637\pi$
$270$		0			0
$271$	71858.5	+	71858.5i	0.978452	+	0.978452i	0.999773	−	0.0213209i	$-0.00678717\pi$
$271$	71858.5	+	71858.5i	0.978452	+	0.978452i	−0.0213209	+	0.999773i	$0.506787\pi$
$272$		−	18807.7i		−	0.254213i
$273$		0			0
$274$	40771.6			0.543072
$275$	−120286.	+	120286.i	−1.59056	+	1.59056i
$276$		0			0
$277$		−	14392.6i		−	0.187577i	−0.995592	−	0.0937884i	$-0.970102\pi$
$277$		−	14392.6i		−	0.187577i	0.995592	−	0.0937884i	$-0.0298977\pi$
$278$	59394.2	−	59394.2i	0.768519	−	0.768519i
$279$		0			0
$280$	44153.4	+	44153.4i	0.563181	+	0.563181i
$281$	80935.8	+	80935.8i	1.02501	+	1.02501i	0.999679	+	0.0253301i	$0.00806367\pi$
$281$	80935.8	+	80935.8i	1.02501	+	1.02501i	0.0253301	+	0.999679i	$0.491936\pi$
$282$		0			0
$283$		−	103285.i		−	1.28963i	−0.764339	−	0.644814i	$-0.776935\pi$
$283$		−	103285.i		−	1.28963i	0.764339	−	0.644814i	$-0.223065\pi$
$284$	−12862.2	−	12862.2i	−0.159470	−	0.159470i
$285$		0			0
$286$	−38664.9	−	75775.5i	−0.472699	−	0.926396i
$287$	−78932.9			−0.958284
$288$		0			0
$289$	−2838.60			−0.0339866
$290$		−	119291.i		−	1.41844i
$291$		0			0
$292$	180.897	−	180.897i	0.00212161	−	0.00212161i
$293$	−112492.	−	112492.i	−1.31035	−	1.31035i	−0.921156	−	0.389193i	$-0.872754\pi$
$293$	−112492.	−	112492.i	−1.31035	−	1.31035i	−0.389193	−	0.921156i	$-0.627246\pi$
$294$		0			0
$295$	−125823.			−1.44582
$296$			9372.09i			0.106968i
$297$		0			0
$298$		−	88833.0i		−	1.00033i
$299$	44733.9	−	22825.8i	0.500373	−	0.255319i
$300$		0			0
$301$	−49357.3	+	49357.3i	−0.544776	+	0.544776i
$302$	−109695.			−1.20274
$303$		0			0
$304$	10606.3	−	10606.3i	0.114767	−	0.114767i
$305$	−170622.	+	170622.i	−1.83415	+	1.83415i
$306$		0			0
$307$	65869.5	+	65869.5i	0.698888	+	0.698888i	0.964171	−	0.265283i	$-0.0854653\pi$
$307$	65869.5	+	65869.5i	0.698888	+	0.698888i	−0.265283	+	0.964171i	$0.585465\pi$
$308$	98817.6			1.04168
$309$		0			0
$310$	57573.9	+	57573.9i	0.599104	+	0.599104i
$311$		−	32921.8i		−	0.340379i	−0.985411	−	0.170190i	$-0.945562\pi$
$311$		−	32921.8i		−	0.340379i	0.985411	−	0.170190i	$-0.0544380\pi$
$312$		0			0
$313$	−67694.8			−0.690982			−0.345491	−	0.938422i	$-0.612288\pi$
$313$	−67694.8			−0.690982			−0.345491	+	0.938422i	$0.612288\pi$
$314$	6805.02	−	6805.02i	0.0690192	−	0.0690192i
$315$		0			0
$316$		−	52612.1i		−	0.526880i
$317$	87722.3	−	87722.3i	0.872954	−	0.872954i	−0.119839	−	0.992793i	$-0.538238\pi$
$317$	87722.3	−	87722.3i	0.872954	−	0.872954i	0.992793	+	0.119839i	$0.0382380\pi$
$318$		0			0
$319$	−133489.	−	133489.i	−1.31179	−	1.31179i
$320$	14394.6	+	14394.6i	0.140572	+	0.140572i
$321$		0			0
$322$			58336.8i			0.562640i
$323$	−48701.3	−	48701.3i	−0.466805	−	0.466805i
$324$		0			0
$325$	143889.	−	73420.1i	1.36226	−	0.695101i
$326$	79329.2			0.746445
$327$		0			0
$328$	−25733.2			−0.239191
$329$			130119.i			1.20213i
$330$		0			0
$331$	−46314.1	+	46314.1i	−0.422725	+	0.422725i	−0.886141	−	0.463416i	$-0.846624\pi$
$331$	−46314.1	+	46314.1i	−0.422725	+	0.422725i	0.463416	+	0.886141i	$0.346624\pi$
$332$	−45531.6	−	45531.6i	−0.413082	−	0.413082i
$333$		0			0
$334$	26915.0			0.241269
$335$		−	177457.i		−	1.58126i
$336$		0			0
$337$			174379.i			1.53545i	0.640782	+	0.767723i	$0.278610\pi$
$337$			174379.i			1.53545i	−0.640782	+	0.767723i	$0.721390\pi$
$338$	12729.8	+	79773.4i	0.111426	+	0.698272i
$339$		0			0
$340$	66095.9	−	66095.9i	0.571764	−	0.571764i
$341$	128853.			1.10812
$342$		0			0
$343$	748.709	−	748.709i	0.00636392	−	0.00636392i
$344$	−16091.1	+	16091.1i	−0.135978	+	0.135978i
$345$		0			0
$346$	64593.7	+	64593.7i	0.539558	+	0.539558i
$347$	55837.1			0.463729			0.231864	−	0.972748i	$-0.425517\pi$
$347$	55837.1			0.463729			0.231864	+	0.972748i	$0.425517\pi$
$348$		0			0
$349$	−30432.8	−	30432.8i	−0.249857	−	0.249857i	0.571055	−	0.820912i	$-0.306534\pi$
$349$	−30432.8	−	30432.8i	−0.249857	−	0.249857i	−0.820912	+	0.571055i	$0.806534\pi$
$350$			187643.i			1.53178i
$351$		0			0
$352$	32215.8			0.260006
$353$	159731.	−	159731.i	1.28186	−	1.28186i	0.342246	−	0.939610i	$-0.388812\pi$
$353$	159731.	−	159731.i	1.28186	−	1.28186i	0.939610	−	0.342246i	$-0.111188\pi$
$354$		0			0
$355$		−	90403.6i		−	0.717347i
$356$	−33948.4	+	33948.4i	−0.267867	+	0.267867i
$357$		0			0
$358$	82348.4	+	82348.4i	0.642524	+	0.642524i
$359$	86021.7	+	86021.7i	0.667451	+	0.667451i	0.957125	−	0.289674i	$-0.0935470\pi$
$359$	86021.7	+	86021.7i	0.667451	+	0.667451i	−0.289674	+	0.957125i	$0.593547\pi$
$360$		0			0
$361$			75392.2i			0.578512i
$362$	63307.1	+	63307.1i	0.483098	+	0.483098i
$363$		0			0
$364$	−89261.6	−	28945.6i	−0.673693	−	0.218464i
$365$	1271.45			0.00954364
$366$		0			0
$367$	−77247.7			−0.573527			−0.286763	−	0.958001i	$-0.592579\pi$
$367$	−77247.7			−0.573527			−0.286763	+	0.958001i	$0.592579\pi$
$368$			19018.6i			0.140437i
$369$		0			0
$370$	−32936.4	+	32936.4i	−0.240587	+	0.240587i
$371$	28209.8	+	28209.8i	0.204952	+	0.204952i
$372$		0			0
$373$	213860.			1.53713			0.768566	−	0.639771i	$-0.220971\pi$
$373$	213860.			1.53713			0.768566	+	0.639771i	$0.220971\pi$
$374$		−	147926.i		−	1.05755i
$375$		0			0
$376$			42420.6i			0.300055i
$377$	81478.9	+	159682.i	0.573274	+	1.12350i
$378$		0			0
$379$	181098.	−	181098.i	1.26077	−	1.26077i	0.310047	−	0.950721i	$-0.399655\pi$
$379$	181098.	−	181098.i	1.26077	−	1.26077i	0.950721	−	0.310047i	$-0.100345\pi$
$380$	74547.7			0.516258
$381$		0			0
$382$	30790.9	−	30790.9i	0.211007	−	0.211007i
$383$	−202157.	+	202157.i	−1.37813	+	1.37813i	−0.530366	+	0.847769i	$0.677946\pi$
$383$	−202157.	+	202157.i	−1.37813	+	1.37813i	−0.847769	+	0.530366i	$0.822054\pi$
$384$		0			0
$385$	347275.	+	347275.i	2.34289	+	2.34289i
$386$	−128996.			−0.865765
$387$		0			0
$388$	−28261.1	−	28261.1i	−0.187727	−	0.187727i
$389$			16045.1i			0.106033i	0.998594	+	0.0530167i	$0.0168836\pi$
$389$			16045.1i			0.106033i	−0.998594	+	0.0530167i	$0.983116\pi$
$390$		0			0
$391$	87327.8			0.571215
$392$	38660.1	−	38660.1i	0.251588	−	0.251588i
$393$		0			0
$394$		−	113467.i		−	0.730930i
$395$	184895.	−	184895.i	1.18504	−	1.18504i
$396$		0			0
$397$	25762.9	+	25762.9i	0.163461	+	0.163461i	0.784098	−	0.620637i	$-0.213126\pi$
$397$	25762.9	+	25762.9i	0.163461	+	0.163461i	−0.620637	+	0.784098i	$0.713126\pi$
$398$	82617.3	+	82617.3i	0.521560	+	0.521560i
$399$		0			0
$400$			61174.0i			0.382338i
$401$	−91271.3	−	91271.3i	−0.567604	−	0.567604i	0.363853	−	0.931457i	$-0.381461\pi$
$401$	−91271.3	−	91271.3i	−0.567604	−	0.567604i	−0.931457	+	0.363853i	$0.881461\pi$
$402$		0			0
$403$	−116393.	−	37743.6i	−0.716664	−	0.232399i
$404$	−144362.			−0.884486
$405$		0			0
$406$	−208239.			−1.26331
$407$			73713.3i			0.444997i
$408$		0			0
$409$	4746.04	−	4746.04i	0.0283716	−	0.0283716i	−0.692779	−	0.721150i	$-0.743614\pi$
$409$	4746.04	−	4746.04i	0.0283716	−	0.0283716i	0.721150	+	0.692779i	$0.243614\pi$
$410$	−90434.2	−	90434.2i	−0.537978	−	0.537978i
$411$		0			0
$412$	17024.7			0.100296
$413$			219642.i			1.28770i
$414$		0			0
$415$		−	320024.i		−	1.85817i
$416$	−29100.5	−	9436.65i	−0.168156	−	0.0545294i
$417$		0			0
$418$	83420.8	−	83420.8i	0.477443	−	0.477443i
$419$	−82509.8			−0.469978			−0.234989	−	0.971998i	$-0.575505\pi$
$419$	−82509.8			−0.469978			−0.234989	+	0.971998i	$0.575505\pi$
$420$		0			0
$421$	159452.	−	159452.i	0.899636	−	0.899636i	−0.0957676	−	0.995404i	$-0.530531\pi$
$421$	159452.	−	159452.i	0.899636	−	0.899636i	0.995404	+	0.0957676i	$0.0305306\pi$
$422$	107396.	−	107396.i	0.603062	−	0.603062i
$423$		0			0
$424$	9196.78	+	9196.78i	0.0511569	+	0.0511569i
$425$	280894.			1.55512
$426$		0			0
$427$	297845.	+	297845.i	1.63356	+	1.63356i
$428$		−	70708.5i		−	0.385997i
$429$		0			0
$430$	−113098.			−0.611672
$431$	191869.	−	191869.i	1.03288	−	1.03288i	0.0334379	−	0.999441i	$-0.489354\pi$
$431$	191869.	−	191869.i	1.03288	−	1.03288i	0.999441	−	0.0334379i	$-0.0106456\pi$
$432$		0			0
$433$			167200.i			0.891783i	0.895087	+	0.445892i	$0.147113\pi$
$433$			167200.i			0.891783i	−0.895087	+	0.445892i	$0.852887\pi$
$434$	100503.	−	100503.i	0.533582	−	0.533582i
$435$		0			0
$436$	20141.1	+	20141.1i	0.105952	+	0.105952i
$437$	49247.3	+	49247.3i	0.257881	+	0.257881i
$438$		0			0
$439$		−	223012.i		−	1.15717i	−0.815621	−	0.578587i	$-0.803604\pi$
$439$		−	223012.i		−	1.15717i	0.815621	−	0.578587i	$-0.196396\pi$
$440$	113216.	+	113216.i	0.584795	+	0.584795i
$441$		0			0
$442$	−43330.4	+	133621.i	−0.221793	+	0.683960i
$443$	17437.9			0.0888559			0.0444280	−	0.999013i	$-0.485853\pi$
$443$	17437.9			0.0888559			0.0444280	+	0.999013i	$0.485853\pi$
$444$		0			0
$445$	−238610.			−1.20495
$446$			159049.i			0.799578i
$447$		0			0
$448$	25127.8	−	25127.8i	0.125198	−	0.125198i
$449$	102553.	+	102553.i	0.508694	+	0.508694i	0.914126	−	0.405431i	$-0.132879\pi$
$449$	102553.	+	102553.i	0.508694	+	0.508694i	−0.405431	+	0.914126i	$0.632879\pi$
$450$		0			0
$451$	−202396.			−0.995060
$452$			15465.5i			0.0756984i
$453$		0			0
$454$		−	55038.0i		−	0.267025i
$455$	−211969.	−	415416.i	−1.02388	−	2.00660i
$456$		0			0
$457$	212786.	−	212786.i	1.01885	−	1.01885i	0.0190328	−	0.999819i	$-0.493941\pi$
$457$	212786.	−	212786.i	1.01885	−	1.01885i	0.999819	−	0.0190328i	$-0.00605869\pi$
$458$	−105044.			−0.500774
$459$		0			0
$460$	−66837.0	+	66837.0i	−0.315865	+	0.315865i
$461$	−163359.	+	163359.i	−0.768674	+	0.768674i	−0.977873	−	0.209199i	$-0.932914\pi$
$461$	−163359.	+	163359.i	−0.768674	+	0.768674i	0.209199	+	0.977873i	$0.432914\pi$
$462$		0			0
$463$	−12062.7	−	12062.7i	−0.0562705	−	0.0562705i	0.678412	−	0.734682i	$-0.262669\pi$
$463$	−12062.7	−	12062.7i	−0.0562705	−	0.0562705i	−0.734682	+	0.678412i	$0.762669\pi$
$464$	−67888.7			−0.315327
$465$		0			0
$466$	82767.6	+	82767.6i	0.381144	+	0.381144i
$467$		−	405742.i		−	1.86044i	−0.367001	−	0.930221i	$-0.619615\pi$
$467$		−	405742.i		−	1.86044i	0.367001	−	0.930221i	$-0.380385\pi$
$468$		0			0
$469$	−309776.			−1.40832
$470$	−149079.	+	149079.i	−0.674871	+	0.674871i
$471$		0			0
$472$			71606.1i			0.321415i
$473$	−126560.	+	126560.i	−0.565683	+	0.565683i
$474$		0			0
$475$	158406.	+	158406.i	0.702077	+	0.702077i
$476$	−115380.	−	115380.i	−0.509233	−	0.509233i
$477$		0			0
$478$			6401.82i			0.0280187i
$479$	−68415.5	−	68415.5i	−0.298183	−	0.298183i	0.542119	−	0.840302i	$-0.317622\pi$
$479$	−68415.5	−	68415.5i	−0.298183	−	0.298183i	−0.840302	+	0.542119i	$0.817622\pi$
$480$		0			0
$481$	21592.1	−	66585.0i	0.0933263	−	0.287797i
$482$	−132115.			−0.568669
$483$		0			0
$484$	136256.			0.581654
$485$		−	198636.i		−	0.844453i
$486$		0			0
$487$	−6839.49	+	6839.49i	−0.0288380	+	0.0288380i	−0.721379	−	0.692541i	$-0.756491\pi$
$487$	−6839.49	+	6839.49i	−0.0288380	+	0.0288380i	0.692541	+	0.721379i	$0.256491\pi$
$488$	97101.3	+	97101.3i	0.407742	+	0.407742i
$489$		0			0
$490$	271727.			1.13172
$491$			317438.i			1.31673i	0.752701	+	0.658363i	$0.228751\pi$
$491$			317438.i			1.31673i	−0.752701	+	0.658363i	$0.771249\pi$
$492$		0			0
$493$			311726.i			1.28256i
$494$	−99789.3	+	50918.1i	−0.408912	+	0.208650i
$495$		0			0
$496$	32765.4	−	32765.4i	0.133184	−	0.133184i
$497$	−157812.			−0.638893
$498$		0			0
$499$	−169318.	+	169318.i	−0.679989	+	0.679989i	−0.959998	−	0.280008i	$-0.909663\pi$
$499$	−169318.	+	169318.i	−0.679989	+	0.679989i	0.280008	+	0.959998i	$0.409663\pi$
$500$	−74412.0	+	74412.0i	−0.297648	+	0.297648i
$501$		0			0
$502$	−32038.6	−	32038.6i	−0.127135	−	0.127135i
$503$	−53395.1			−0.211040			−0.105520	−	0.994417i	$-0.533651\pi$
$503$	−53395.1			−0.211040			−0.105520	+	0.994417i	$0.533651\pi$
$504$		0			0
$505$	−507333.	−	507333.i	−1.98935	−	1.98935i
$506$			149585.i			0.584233i
$507$		0			0
$508$	−62098.1			−0.240630
$509$	191977.	−	191977.i	0.740992	−	0.740992i	−0.231777	−	0.972769i	$-0.574454\pi$
$509$	191977.	−	191977.i	0.740992	−	0.740992i	0.972769	+	0.231777i	$0.0744539\pi$
$510$		0			0
$511$		−	2219.50i		−	0.00849989i
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−103703.	−	103703.i	−0.392522	−	0.392522i
$515$	59829.8	+	59829.8i	0.225581	+	0.225581i
$516$		0			0
$517$			333646.i			1.24826i
$518$	57495.2	+	57495.2i	0.214275	+	0.214275i
$519$		0			0
$520$	−69104.6	−	135431.i	−0.255565	−	0.500855i
$521$	96837.2			0.356752			0.178376	−	0.983962i	$-0.442916\pi$
$521$	96837.2			0.356752			0.178376	+	0.983962i	$0.442916\pi$
$522$		0			0
$523$	99463.6			0.363631			0.181815	−	0.983333i	$-0.441803\pi$
$523$	99463.6			0.363631			0.181815	+	0.983333i	$0.441803\pi$
$524$			83742.1i			0.304987i
$525$		0			0
$526$	−225168.	+	225168.i	−0.813833	+	0.813833i
$527$	−150450.	−	150450.i	−0.541714	−	0.541714i
$528$		0			0
$529$	191534.			0.684439
$530$			64640.6i			0.230120i
$531$		0			0
$532$		−	130134.i		−	0.459797i
$533$	182824.	+	59285.8i	0.643544	+	0.208687i
$534$		0			0
$535$	248491.	−	248491.i	0.868168	−	0.868168i
$536$	−100991.			−0.351523
$537$		0			0
$538$	−25098.8	+	25098.8i	−0.0867139	+	0.0867139i
$539$	304069.	−	304069.i	1.04663	−	1.04663i
$540$		0			0
$541$	−78592.6	−	78592.6i	−0.268526	−	0.268526i	0.559980	−	0.828506i	$-0.310809\pi$
$541$	−78592.6	−	78592.6i	−0.268526	−	0.268526i	−0.828506	+	0.559980i	$0.810809\pi$
$542$	287434.			0.978452
$543$		0			0
$544$	−37615.4	−	37615.4i	−0.127106	−	0.127106i
$545$			141564.i			0.476607i
$546$		0			0
$547$	−557039.			−1.86171			−0.930853	−	0.365394i	$-0.880934\pi$
$547$	−557039.			−1.86171			−0.930853	+	0.365394i	$0.880934\pi$
$548$	81543.3	−	81543.3i	0.271536	−	0.271536i
$549$		0			0
$550$			481146.i			1.59056i
$551$	−175793.	+	175793.i	−0.579027	+	0.579027i
$552$		0			0
$553$	−322761.	−	322761.i	−1.05543	−	1.05543i
$554$	−28785.2	−	28785.2i	−0.0937884	−	0.0937884i
$555$		0			0
$556$		−	237577.i		−	0.768519i
$557$	276263.	+	276263.i	0.890455	+	0.890455i	0.994566	−	0.104111i	$-0.0331997\pi$
$557$	276263.	+	276263.i	0.890455	+	0.890455i	−0.104111	+	0.994566i	$0.533200\pi$
$558$		0			0
$559$	151393.	−	77249.2i	0.484487	−	0.247212i
$560$	176614.			0.563181
$561$		0			0
$562$	323743.			1.02501
$563$		−	147215.i		−	0.464446i	−0.972663	−	0.232223i	$-0.925400\pi$
$563$		−	147215.i		−	0.464446i	0.972663	−	0.232223i	$-0.0746000\pi$
$564$		0			0
$565$	−54350.5	+	54350.5i	−0.170258	+	0.170258i
$566$	−206570.	−	206570.i	−0.644814	−	0.644814i
$567$		0			0
$568$	−51448.9			−0.159470
$569$		−	537852.i		−	1.66126i	−0.556824	−	0.830631i	$-0.687980\pi$
$569$		−	537852.i		−	1.66126i	0.556824	−	0.830631i	$-0.312020\pi$
$570$		0			0
$571$			484104.i			1.48480i	0.669959	+	0.742398i	$0.266312\pi$
$571$			484104.i			1.48480i	−0.669959	+	0.742398i	$0.733688\pi$
$572$	−228881.	−	74221.1i	−0.699548	−	0.226848i
$573$		0			0
$574$	−157866.	+	157866.i	−0.479142	+	0.479142i
$575$	−284043.			−0.859110
$576$		0			0
$577$	2587.79	−	2587.79i	0.00777280	−	0.00777280i	−0.703210	−	0.710982i	$-0.748250\pi$
$577$	2587.79	−	2587.79i	0.00777280	−	0.00777280i	0.710982	+	0.703210i	$0.248250\pi$
$578$	−5677.20	+	5677.20i	−0.0169933	+	0.0169933i
$579$		0			0
$580$	−238582.	−	238582.i	−0.709220	−	0.709220i
$581$	−558647.			−1.65495
$582$		0			0
$583$	72334.5	+	72334.5i	0.212818	+	0.212818i
$584$		−	723.586i		−	0.00212161i
$585$		0			0
$586$	−449969.			−1.31035
$587$	−164714.	+	164714.i	−0.478029	+	0.478029i	−0.904501	−	0.426472i	$-0.859756\pi$
$587$	−164714.	+	164714.i	−0.478029	+	0.478029i	0.426472	+	0.904501i	$0.359756\pi$
$588$		0			0
$589$		−	169688.i		−	0.489125i
$590$	−251646.	+	251646.i	−0.722912	+	0.722912i
$591$		0			0
$592$	18744.2	+	18744.2i	0.0534839	+	0.0534839i
$593$	−155468.	−	155468.i	−0.442110	−	0.442110i	0.450611	−	0.892721i	$-0.351206\pi$
$593$	−155468.	−	155468.i	−0.442110	−	0.442110i	−0.892721	+	0.450611i	$0.851206\pi$
$594$		0			0
$595$		−	810960.i		−	2.29069i
$596$	−177666.	−	177666.i	−0.500163	−	0.500163i
$597$		0			0
$598$	43816.2	−	135119.i	0.122527	−	0.377846i
$599$	−254077.			−0.708127			−0.354063	−	0.935221i	$-0.615200\pi$
$599$	−254077.			−0.708127			−0.354063	+	0.935221i	$0.615200\pi$
$600$		0			0
$601$	233247.			0.645755			0.322877	−	0.946441i	$-0.395350\pi$
$601$	233247.			0.645755			0.322877	+	0.946441i	$0.395350\pi$
$602$			197429.i			0.544776i
$603$		0			0
$604$	−219390.	+	219390.i	−0.601372	+	0.601372i
$605$	478845.	+	478845.i	1.30823	+	1.30823i
$606$		0			0
$607$	−406297.			−1.10272			−0.551361	−	0.834267i	$-0.685891\pi$
$607$	−406297.			−1.10272			−0.551361	+	0.834267i	$0.685891\pi$
$608$		−	42425.3i		−	0.114767i
$609$		0			0
$610$			682487.i			1.83415i
$611$	97731.5	−	301382.i	0.261790	−	0.807299i
$612$		0			0
$613$	414689.	−	414689.i	1.10357	−	1.10357i	0.109599	−	0.993976i	$-0.465043\pi$
$613$	414689.	−	414689.i	1.10357	−	1.10357i	0.993976	−	0.109599i	$-0.0349566\pi$
$614$	263478.			0.698888
$615$		0			0
$616$	197635.	−	197635.i	0.520838	−	0.520838i
$617$	22163.9	−	22163.9i	0.0582204	−	0.0582204i	−0.677397	−	0.735618i	$-0.736892\pi$
$617$	22163.9	−	22163.9i	0.0582204	−	0.0582204i	0.735618	+	0.677397i	$0.236892\pi$
$618$		0			0
$619$	197408.	+	197408.i	0.515209	+	0.515209i	0.916118	−	0.400909i	$-0.131306\pi$
$619$	197408.	+	197408.i	0.515209	+	0.515209i	−0.400909	+	0.916118i	$0.631306\pi$
$620$	230295.			0.599104
$621$		0			0
$622$	−65843.7	−	65843.7i	−0.170190	−	0.170190i
$623$			416529.i			1.07317i
$624$		0			0
$625$	74389.6			0.190437
$626$	−135390.	+	135390.i	−0.345491	+	0.345491i
$627$		0			0
$628$		−	27220.1i		−	0.0690192i
$629$	86068.1	−	86068.1i	0.217541	−	0.217541i
$630$		0			0
$631$	462597.	+	462597.i	1.16183	+	1.16183i	0.984074	+	0.177761i	$0.0568854\pi$
$631$	462597.	+	462597.i	1.16183	+	1.16183i	0.177761	+	0.984074i	$0.443115\pi$
$632$	−105224.	−	105224.i	−0.263440	−	0.263440i
$633$		0			0
$634$		−	350889.i		−	0.872954i
$635$	−218232.	−	218232.i	−0.541215	−	0.541215i
$636$		0			0
$637$	−363732.	+	185597.i	−0.896403	+	0.457395i
$638$	−533958.			−1.31179
$639$		0			0
$640$	57578.4			0.140572
$641$		−	72292.1i		−	0.175944i	−0.996123	−	0.0879721i	$-0.971961\pi$
$641$		−	72292.1i		−	0.175944i	0.996123	−	0.0879721i	$-0.0280386\pi$
$642$		0			0
$643$	−445366.	+	445366.i	−1.07720	+	1.07720i	−0.0804383	+	0.996760i	$0.525632\pi$
$643$	−445366.	+	445366.i	−1.07720	+	1.07720i	−0.996760	+	0.0804383i	$0.974368\pi$
$644$	116674.	+	116674.i	0.281320	+	0.281320i
$645$		0			0
$646$	−194805.			−0.466805
$647$			535918.i			1.28023i	0.768277	+	0.640117i	$0.221114\pi$
$647$			535918.i			1.28023i	−0.768277	+	0.640117i	$0.778886\pi$
$648$		0			0
$649$			563196.i			1.33712i
$650$	140937.	−	434617.i	0.333578	−	1.02868i
$651$		0			0
$652$	158658.	−	158658.i	0.373222	−	0.373222i
$653$	59790.9			0.140220			0.0701098	−	0.997539i	$-0.477665\pi$
$653$	59790.9			0.140220			0.0701098	+	0.997539i	$0.477665\pi$
$654$		0			0
$655$	−294295.	+	294295.i	−0.685963	+	0.685963i
$656$	−51466.3	+	51466.3i	−0.119596	+	0.119596i
$657$		0			0
$658$	260239.	+	260239.i	0.601063	+	0.601063i
$659$	−254900.			−0.586948			−0.293474	−	0.955967i	$-0.594811\pi$
$659$	−254900.			−0.586948			−0.293474	+	0.955967i	$0.594811\pi$
$660$		0			0
$661$	90948.6	+	90948.6i	0.208158	+	0.208158i	0.803484	−	0.595326i	$-0.202977\pi$
$661$	90948.6	+	90948.6i	0.208158	+	0.208158i	−0.595326	+	0.803484i	$0.702977\pi$
$662$			185257.i			0.422725i
$663$		0			0
$664$	−182126.			−0.413082
$665$	457330.	−	457330.i	1.03416	−	1.03416i
$666$		0			0
$667$		−	315221.i		−	0.708538i
$668$	53830.0	−	53830.0i	0.120634	−	0.120634i
$669$		0			0
$670$	−354914.	−	354914.i	−0.790630	−	0.790630i
$671$	763721.	+	763721.i	1.69625	+	1.69625i
$672$		0			0
$673$		−	2365.55i		−	0.00522279i	−0.999997	−	0.00261140i	$-0.999169\pi$
$673$		−	2365.55i		−	0.00522279i	0.999997	−	0.00261140i	$-0.000831234\pi$
$674$	348758.	+	348758.i	0.767723	+	0.767723i
$675$		0			0
$676$	185006.	+	134087.i	0.404849	+	0.293423i
$677$	229195.			0.500067			0.250034	−	0.968237i	$-0.419558\pi$
$677$	229195.			0.500067			0.250034	+	0.968237i	$0.419558\pi$
$678$		0			0
$679$	−346748.			−0.752098
$680$		−	264384.i		−	0.571764i
$681$		0			0
$682$	257706.	−	257706.i	0.554060	−	0.554060i
$683$	147044.	+	147044.i	0.315214	+	0.315214i	0.846926	−	0.531711i	$-0.178451\pi$
$683$	147044.	+	147044.i	0.315214	+	0.315214i	−0.531711	+	0.846926i	$0.678451\pi$
$684$		0			0
$685$	573136.			1.22145
$686$		−	2994.83i		−	0.00636392i
$687$		0			0
$688$			64364.5i			0.135978i
$689$	−44151.3	−	86527.7i	−0.0930048	−	0.182271i
$690$		0			0
$691$	−238903.	+	238903.i	−0.500341	+	0.500341i	−0.911544	−	0.411203i	$-0.865109\pi$
$691$	−238903.	+	238903.i	−0.500341	+	0.500341i	0.411203	+	0.911544i	$0.365109\pi$
$692$	258375.			0.539558
$693$		0			0
$694$	111674.	−	111674.i	0.231864	−	0.231864i
$695$	834917.	−	834917.i	1.72852	−	1.72852i
$696$		0			0
$697$	236319.	+	236319.i	0.486444	+	0.486444i
$698$	−121731.			−0.249857
$699$		0			0
$700$	375286.	+	375286.i	0.765889	+	0.765889i
$701$			927743.i			1.88796i	0.330009	+	0.943978i	$0.392948\pi$
$701$			927743.i			1.88796i	−0.330009	+	0.943978i	$0.607052\pi$
$702$		0			0
$703$	97073.7			0.196422
$704$	64431.7	−	64431.7i	0.130003	−	0.130003i
$705$		0			0
$706$		−	638923.i		−	1.28186i
$707$	−885622.	+	885622.i	−1.77178	+	1.77178i
$708$		0			0
$709$	655343.	+	655343.i	1.30369	+	1.30369i	0.925882	+	0.377813i	$0.123324\pi$
$709$	655343.	+	655343.i	1.30369	+	1.30369i	0.377813	+	0.925882i	$0.376676\pi$
$710$	−180807.	−	180807.i	−0.358673	−	0.358673i
$711$		0			0
$712$			135794.i			0.267867i
$713$	152136.	+	152136.i	0.299264	+	0.299264i
$714$		0			0
$715$	−543521.	−	1.06519e6i	−1.06317	−	2.08361i
$716$	329394.			0.642524
$717$		0			0
$718$	344087.			0.667451
$719$		−	215165.i		−	0.416211i	−0.978106	−	0.208106i	$-0.933270\pi$
$719$		−	215165.i		−	0.416211i	0.978106	−	0.208106i	$-0.0667298\pi$
$720$		0			0
$721$	104441.	−	104441.i	0.200910	−	0.200910i
$722$	150784.	+	150784.i	0.289256	+	0.289256i
$723$		0			0
$724$	253228.			0.483098
$725$		−	1.01392e6i		−	1.92898i
$726$		0			0
$727$		−	803738.i		−	1.52071i	−0.649510	−	0.760353i	$-0.725026\pi$
$727$		−	803738.i		−	1.52071i	0.649510	−	0.760353i	$-0.274974\pi$
$728$	−236414.	+	120632.i	−0.446078	+	0.227614i
$729$		0			0
$730$	2542.90	−	2542.90i	0.00477182	−	0.00477182i
$731$	295544.			0.553079
$732$		0			0
$733$	200160.	−	200160.i	0.372537	−	0.372537i	−0.495864	−	0.868400i	$-0.665148\pi$
$733$	200160.	−	200160.i	0.372537	−	0.372537i	0.868400	+	0.495864i	$0.165148\pi$
$734$	−154495.	+	154495.i	−0.286763	+	0.286763i
$735$		0			0
$736$	38037.1	+	38037.1i	0.0702185	+	0.0702185i
$737$	−794315.			−1.46237
$738$		0			0
$739$	424211.	+	424211.i	0.776771	+	0.776771i	0.979280	−	0.202509i	$-0.0649096\pi$
$739$	424211.	+	424211.i	0.776771	+	0.776771i	−0.202509	+	0.979280i	$0.564910\pi$
$740$			131746.i			0.240587i
$741$		0			0
$742$	112839.			0.204952
$743$	130672.	−	130672.i	0.236704	−	0.236704i	−0.578780	−	0.815484i	$-0.696471\pi$
$743$	130672.	−	130672.i	0.236704	−	0.236704i	0.815484	+	0.578780i	$0.196471\pi$
$744$		0			0
$745$		−	1.24875e6i		−	2.24989i
$746$	427719.	−	427719.i	0.768566	−	0.768566i
$747$		0			0
$748$	−295852.	−	295852.i	−0.528776	−	0.528776i
$749$	−433777.	−	433777.i	−0.773220	−	0.773220i
$750$		0			0
$751$			742621.i			1.31670i	0.752711	+	0.658351i	$0.228746\pi$
$751$			742621.i			1.31670i	−0.752711	+	0.658351i	$0.771254\pi$
$752$	84841.2	+	84841.2i	0.150028	+	0.150028i
$753$		0			0
$754$	482322.	+	156407.i	0.848388	+	0.275114i
$755$	−1.54201e6			−2.70516
$756$		0			0
$757$	−382172.			−0.666910			−0.333455	−	0.942766i	$-0.608215\pi$
$757$	−382172.			−0.666910			−0.333455	+	0.942766i	$0.608215\pi$
$758$		−	724392.i		−	1.26077i
$759$		0			0
$760$	149095.	−	149095.i	0.258129	−	0.258129i
$761$	−335972.	−	335972.i	−0.580141	−	0.580141i	0.354801	−	0.934942i	$-0.384549\pi$
$761$	−335972.	−	335972.i	−0.580141	−	0.580141i	−0.934942	+	0.354801i	$0.884549\pi$
$762$		0			0
$763$	247121.			0.424482
$764$		−	123164.i		−	0.211007i
$765$		0			0
$766$			808629.i			1.37813i
$767$	164971.	−	508733.i	0.280425	−	0.864767i
$768$		0			0
$769$	−90354.5	+	90354.5i	−0.152791	+	0.152791i	−0.779363	−	0.626572i	$-0.784457\pi$
$769$	−90354.5	+	90354.5i	−0.152791	+	0.152791i	0.626572	+	0.779363i	$0.284457\pi$
$770$	1.38910e6			2.34289
$771$		0			0
$772$	−257991.	+	257991.i	−0.432883	+	0.432883i
$773$	−511378.	+	511378.i	−0.855821	+	0.855821i	−0.990843	−	0.135021i	$-0.956890\pi$
$773$	−511378.	+	511378.i	−0.855821	+	0.855821i	0.135021	+	0.990843i	$0.456890\pi$
$774$		0			0
$775$	489354.	+	489354.i	0.814741	+	0.814741i
$776$	−113044.			−0.187727
$777$		0			0
$778$	32090.1	+	32090.1i	0.0530167	+	0.0530167i
$779$			266537.i			0.439221i
$780$		0			0
$781$	−404656.			−0.663412
$782$	174656.	−	174656.i	0.285607	−	0.285607i
$783$		0			0
$784$		−	154640.i		−	0.251588i
$785$	95659.7	−	95659.7i	0.155235	−	0.155235i
$786$		0			0
$787$	−305280.	−	305280.i	−0.492888	−	0.492888i	0.416327	−	0.909215i	$-0.363317\pi$
$787$	−305280.	−	305280.i	−0.492888	−	0.492888i	−0.909215	+	0.416327i	$0.863317\pi$
$788$	−226933.	−	226933.i	−0.365465	−	0.365465i
$789$		0			0
$790$		−	739580.i		−	1.18504i
$791$	94876.5	+	94876.5i	0.151637	+	0.151637i
$792$		0			0
$793$	−466158.	−	913575.i	−0.741287	−	1.45277i
$794$	103052.			0.163461
$795$		0			0
$796$	330469.			0.521560
$797$			304571.i			0.479481i	0.970837	+	0.239740i	$0.0770623\pi$
$797$			304571.i			0.479481i	−0.970837	+	0.239740i	$0.922938\pi$
$798$		0			0
$799$	389567.	−	389567.i	0.610223	−	0.610223i
$800$	122348.	+	122348.i	0.191169	+	0.191169i
$801$		0			0
$802$	−365085.			−0.567604
$803$		−	5691.15i		−	0.00882610i
$804$		0			0
$805$			820053.i			1.26546i
$806$	−308273.	+	157298.i	−0.474531	+	0.242133i
$807$		0			0
$808$	−288724.	+	288724.i	−0.442243	+	0.442243i
$809$	685883.			1.04798			0.523990	−	0.851725i	$-0.324443\pi$
$809$	685883.			1.04798			0.523990	+	0.851725i	$0.324443\pi$
$810$		0			0
$811$	−815652.	+	815652.i	−1.24012	+	1.24012i	−0.280166	+	0.959951i	$0.590390\pi$
$811$	−815652.	+	815652.i	−1.24012	+	1.24012i	−0.959951	+	0.280166i	$0.909610\pi$
$812$	−416478.	+	416478.i	−0.631656	+	0.631656i
$813$		0			0
$814$	147427.	+	147427.i	0.222499	+	0.222499i
$815$	1.11515e6			1.67887
$816$		0			0
$817$	166668.	+	166668.i	0.249693	+	0.249693i
$818$		−	18984.1i		−	0.0283716i
$819$		0			0
$820$	−361737.			−0.537978
$821$	−12855.5	+	12855.5i	−0.0190723	+	0.0190723i	−0.716579	−	0.697506i	$-0.754293\pi$
$821$	−12855.5	+	12855.5i	−0.0190723	+	0.0190723i	0.697506	+	0.716579i	$0.254293\pi$
$822$		0			0
$823$			94810.5i			0.139977i	0.997548	+	0.0699885i	$0.0222963\pi$
$823$			94810.5i			0.139977i	−0.997548	+	0.0699885i	$0.977704\pi$
$824$	34049.3	−	34049.3i	0.0501480	−	0.0501480i
$825$		0			0
$826$	439283.	+	439283.i	0.643850	+	0.643850i
$827$	−113400.	−	113400.i	−0.165807	−	0.165807i	0.619327	−	0.785134i	$-0.287406\pi$
$827$	−113400.	−	113400.i	−0.165807	−	0.165807i	−0.785134	+	0.619327i	$0.787406\pi$
$828$		0			0
$829$			15161.7i			0.0220616i	0.999939	+	0.0110308i	$0.00351129\pi$
$829$			15161.7i			0.0220616i	−0.999939	+	0.0110308i	$0.996489\pi$
$830$	−640048.	−	640048.i	−0.929086	−	0.929086i
$831$		0			0
$832$	−77074.2	+	39327.6i	−0.111343	+	0.0568134i
$833$	−710065.			−1.02331
$834$		0			0
$835$	378350.			0.542651
$836$		−	333683.i		−	0.477443i
$837$		0			0
$838$	−165020.	+	165020.i	−0.234989	+	0.234989i
$839$	398624.	+	398624.i	0.566290	+	0.566290i	0.931087	−	0.364797i	$-0.118862\pi$
$839$	398624.	+	398624.i	0.566290	+	0.566290i	−0.364797	+	0.931087i	$0.618862\pi$
$840$		0			0
$841$	417933.			0.590901
$842$		−	637810.i		−	0.899636i
$843$		0			0
$844$		−	429582.i		−	0.603062i
$845$	178946.	+	1.12139e6i	0.250615	+	1.57052i
$846$		0			0
$847$	835892.	−	835892.i	1.16515	−	1.16515i
$848$	36787.1			0.0511569
$849$		0			0
$850$	561788.	−	561788.i	0.777561	−	0.777561i
$851$	−87033.0	+	87033.0i	−0.120178	+	0.120178i
$852$		0			0
$853$	−160276.	−	160276.i	−0.220277	−	0.220277i	0.588338	−	0.808615i	$-0.299782\pi$
$853$	−160276.	−	160276.i	−0.220277	−	0.220277i	−0.808615	+	0.588338i	$0.799782\pi$
$854$	1.19138e6			1.63356
$855$		0			0
$856$	−141417.	−	141417.i	−0.192999	−	0.192999i
$857$		−	65742.3i		−	0.0895124i	−0.998998	−	0.0447562i	$-0.985749\pi$
$857$		−	65742.3i		−	0.0895124i	0.998998	−	0.0447562i	$-0.0142511\pi$
$858$		0			0
$859$	−214439.			−0.290614			−0.145307	−	0.989387i	$-0.546417\pi$
$859$	−214439.			−0.290614			−0.145307	+	0.989387i	$0.546417\pi$
$860$	−226196.	+	226196.i	−0.305836	+	0.305836i
$861$		0			0
$862$		−	767474.i		−	1.03288i
$863$	735390.	−	735390.i	0.987407	−	0.987407i	−0.0125152	−	0.999922i	$-0.503984\pi$
$863$	735390.	−	735390.i	0.987407	−	0.987407i	0.999922	+	0.0125152i	$0.00398381\pi$
$864$		0			0
$865$	908009.	+	908009.i	1.21355	+	1.21355i
$866$	334399.	+	334399.i	0.445892	+	0.445892i
$867$		0			0
$868$		−	402014.i		−	0.533582i
$869$	−827609.	−	827609.i	−1.09594	−	1.09594i
$870$		0			0
$871$	717502.	+	232670.i	0.945773	+	0.306694i
$872$	80564.5			0.105952
$873$		0			0
$874$	196989.			0.257881
$875$			912994.i			1.19248i
$876$		0			0
$877$	−704397.	+	704397.i	−0.915838	+	0.915838i	−0.996723	−	0.0808858i	$-0.974225\pi$
$877$	−704397.	+	704397.i	−0.915838	+	0.915838i	0.0808858	+	0.996723i	$0.474225\pi$
$878$	−446023.	−	446023.i	−0.578587	−	0.578587i
$879$		0			0
$880$	452865.			0.584795
$881$			547899.i			0.705909i	0.935641	+	0.352954i	$0.114823\pi$
$881$			547899.i			0.705909i	−0.935641	+	0.352954i	$0.885177\pi$
$882$		0			0
$883$		−	949898.i		−	1.21830i	−0.793054	−	0.609152i	$-0.791510\pi$
$883$		−	949898.i		−	1.21830i	0.793054	−	0.609152i	$-0.208490\pi$
$884$	180581.	+	353903.i	0.231083	+	0.452877i
$885$		0			0
$886$	34875.8	−	34875.8i	0.0444280	−	0.0444280i
$887$	−587902.			−0.747236			−0.373618	−	0.927583i	$-0.621883\pi$
$887$	−587902.			−0.747236			−0.373618	+	0.927583i	$0.621883\pi$
$888$		0			0
$889$	−380954.	+	380954.i	−0.482025	+	0.482025i
$890$	−477221.	+	477221.i	−0.602476	+	0.602476i
$891$		0			0
$892$	318098.	+	318098.i	0.399789	+	0.399789i
$893$	439382.			0.550984
$894$		0			0
$895$	1.15759e6	+	1.15759e6i	1.44514	+	1.44514i
$896$		−	100511.i		−	0.125198i
$897$		0			0
$898$	410213.			0.508694
$899$	−543067.	+	543067.i	−0.671945	+	0.671945i
$900$		0			0
$901$		−	168916.i		−	0.208076i
$902$	−404793.	+	404793.i	−0.497530	+	0.497530i
$903$		0			0
$904$	30931.0	+	30931.0i	0.0378492	+	0.0378492i
$905$	889922.	+	889922.i	1.08656	+	1.08656i
$906$		0			0
$907$			490495.i			0.596239i	0.954529	+	0.298119i	$0.0963594\pi$
$907$			490495.i			0.596239i	−0.954529	+	0.298119i	$0.903641\pi$
$908$	−110076.	−	110076.i	−0.133512	−	0.133512i
$909$		0			0
$910$	−1.25477e6	−	406895.i	−1.51524	−	0.491359i
$911$	265333.			0.319708			0.159854	−	0.987141i	$-0.448898\pi$
$911$	265333.			0.319708			0.159854	+	0.987141i	$0.448898\pi$
$912$		0			0
$913$	−1.43246e6			−1.71846
$914$		−	851145.i		−	1.01885i
$915$		0			0
$916$	−210089.	+	210089.i	−0.250387	+	0.250387i
$917$	513734.	+	513734.i	0.610942	+	0.610942i
$918$		0			0
$919$	1.16310e6			1.37717			0.688584	−	0.725156i	$-0.258232\pi$
$919$	1.16310e6			1.37717			0.688584	+	0.725156i	$0.258232\pi$
$920$			267348.i			0.315865i
$921$		0			0
$922$			653437.i			0.768674i
$923$	365524.	+	118532.i	0.429055	+	0.139133i
$924$		0			0
$925$	−279946.	+	279946.i	−0.327183	+	0.327183i
$926$	−48250.6			−0.0562705
$927$		0			0
$928$	−135777.	+	135777.i	−0.157664	+	0.157664i
$929$	−452245.	+	452245.i	−0.524013	+	0.524013i	−0.918781	−	0.394768i	$-0.870825\pi$
$929$	−452245.	+	452245.i	−0.524013	+	0.524013i	0.394768	+	0.918781i	$0.370825\pi$
$930$		0			0
$931$	−400431.	−	400431.i	−0.461986	−	0.461986i
$932$	331070.			0.381144
$933$		0			0
$934$	−811484.	−	811484.i	−0.930221	−	0.930221i
$935$		−	2.07943e6i		−	2.37860i
$936$		0			0
$937$	−748585.			−0.852633			−0.426316	−	0.904574i	$-0.640189\pi$
$937$	−748585.			−0.852633			−0.426316	+	0.904574i	$0.640189\pi$
$938$	−619553.	+	619553.i	−0.704162	+	0.704162i
$939$		0			0
$940$			596316.i			0.674871i
$941$	−39986.3	+	39986.3i	−0.0451577	+	0.0451577i	−0.729325	−	0.684167i	$-0.760166\pi$
$941$	−39986.3	+	39986.3i	−0.0451577	+	0.0451577i	0.684167	+	0.729325i	$0.260166\pi$
$942$		0			0
$943$	−238968.	−	238968.i	−0.268731	−	0.268731i
$944$	143212.	+	143212.i	0.160707	+	0.160707i
$945$		0			0
$946$			506239.i			0.565683i
$947$	811733.	+	811733.i	0.905135	+	0.905135i	0.995875	−	0.0907396i	$-0.0289231\pi$
$947$	811733.	+	811733.i	0.905135	+	0.905135i	−0.0907396	+	0.995875i	$0.528923\pi$
$948$		0			0
$949$	−1667.05	+	5140.79i	−0.00185104	+	0.00570818i
$950$	633624.			0.702077
$951$		0			0
$952$	−461520.			−0.509233
$953$		−	783349.i		−	0.862521i	−0.902227	−	0.431260i	$-0.858069\pi$
$953$		−	783349.i		−	0.862521i	0.902227	−	0.431260i	$-0.141931\pi$
$954$		0			0
$955$	432835.	−	432835.i	0.474587	−	0.474587i
$956$	12803.6	+	12803.6i	0.0140093	+	0.0140093i
$957$		0			0
$958$	−273662.			−0.298183
$959$		−	1.00049e6i		−	1.08787i
$960$		0			0
$961$			399315.i			0.432384i
$962$	−89985.9	−	176354.i	−0.0972354	−	0.190562i
$963$		0			0
$964$	−264231.	+	264231.i	−0.284335	+	0.284335i
$965$	−1.81332e6			−1.94724
$966$		0			0
$967$	374447.	−	374447.i	0.400440	−	0.400440i	−0.477948	−	0.878388i	$-0.658619\pi$
$967$	374447.	−	374447.i	0.400440	−	0.400440i	0.878388	+	0.477948i	$0.158619\pi$
$968$	272512.	−	272512.i	0.290827	−	0.290827i
$969$		0			0
$970$	−397273.	−	397273.i	−0.422226	−	0.422226i
$971$	−93108.8			−0.0987535			−0.0493767	−	0.998780i	$-0.515724\pi$
$971$	−93108.8			−0.0987535			−0.0493767	+	0.998780i	$0.515724\pi$
$972$		0			0
$973$	−1.45747e6	−	1.45747e6i	−1.53948	−	1.53948i
$974$			27358.0i			0.0288380i
$975$		0			0
$976$	388405.			0.407742
$977$	360353.	−	360353.i	0.377519	−	0.377519i	−0.492687	−	0.870206i	$-0.663985\pi$
$977$	360353.	−	360353.i	0.377519	−	0.377519i	0.870206	+	0.492687i	$0.163985\pi$
$978$		0			0
$979$			1.06804e6i			1.11436i
$980$	543453.	−	543453.i	0.565862	−	0.565862i
$981$		0			0
$982$	634875.	+	634875.i	0.658363	+	0.658363i
$983$	−525101.	−	525101.i	−0.543420	−	0.543420i	0.381110	−	0.924530i	$-0.375542\pi$
$983$	−525101.	−	525101.i	−0.543420	−	0.543420i	−0.924530	+	0.381110i	$0.875542\pi$
$984$		0			0
$985$		−	1.59503e6i		−	1.64398i
$986$	623452.	+	623452.i	0.641282	+	0.641282i
$987$		0			0
$988$	−97742.3	+	301415.i	−0.100131	+	0.308781i
$989$	−298857.			−0.305542
$990$		0			0
$991$	−1.55237e6			−1.58069			−0.790347	−	0.612660i	$-0.790100\pi$
$991$	−1.55237e6			−1.58069			−0.790347	+	0.612660i	$0.790100\pi$
$992$		−	131062.i		−	0.133184i
$993$		0			0
$994$	−315625.	+	315625.i	−0.319447	+	0.319447i
$995$	1.16137e6	+	1.16137e6i	1.17307	+	1.17307i
$996$		0			0
$997$	−1.39961e6			−1.40805			−0.704024	−	0.710176i	$-0.748615\pi$
$997$	−1.39961e6			−1.40805			−0.704024	+	0.710176i	$0.748615\pi$
$998$			677272.i			0.679989i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.5.i.b.109.3		6
3.2	odd	2		26.5.d.a.5.2	✓	6
12.11	even	2		208.5.t.b.161.2		6
13.8	odd	4	inner	234.5.i.b.73.3		6
39.5	even	4		338.5.d.d.99.2		6
39.8	even	4		26.5.d.a.21.2	yes	6
39.38	odd	2		338.5.d.d.239.2		6
156.47	odd	4		208.5.t.b.177.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.d.a.5.2	✓	6	3.2	odd	2
26.5.d.a.21.2	yes	6	39.8	even	4
208.5.t.b.161.2		6	12.11	even	2
208.5.t.b.177.2		6	156.47	odd	4
234.5.i.b.73.3		6	13.8	odd	4	inner
234.5.i.b.109.3		6	1.1	even	1	trivial
338.5.d.d.99.2		6	39.5	even	4
338.5.d.d.239.2		6	39.38	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	234.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{2} -8.00000i q^{4} +(28.1144 - 28.1144i) q^{5} +(-49.0778 - 49.0778i) q^{7} +(-16.0000 - 16.0000i) q^{8} -112.458i q^{10} +(-125.843 - 125.843i) q^{11} +(76.8118 + 150.536i) q^{13} -196.311 q^{14} -64.0000 q^{16} +293.870i q^{17} +(-165.724 + 165.724i) q^{19} +(-224.916 - 224.916i) q^{20} -503.372 q^{22} -297.165i q^{23} -955.844i q^{25} +(454.695 + 147.448i) q^{26} +(-392.622 + 392.622i) q^{28} +1060.76 q^{29} +(-511.960 + 511.960i) q^{31} +(-128.000 + 128.000i) q^{32} +(587.740 + 587.740i) q^{34} -2759.59 q^{35} +(-292.878 - 292.878i) q^{37} +662.895i q^{38} -899.662 q^{40} +(804.161 - 804.161i) q^{41} -1005.69i q^{43} +(-1006.74 + 1006.74i) q^{44} +(-594.330 - 594.330i) q^{46} +(-1325.64 - 1325.64i) q^{47} +2416.26i q^{49} +(-1911.69 - 1911.69i) q^{50} +(1204.28 - 614.494i) q^{52} -574.799 q^{53} -7076.02 q^{55} +1570.49i q^{56} +(2121.52 - 2121.52i) q^{58} +(-2237.69 - 2237.69i) q^{59} -6068.83 q^{61} +2047.84i q^{62} +512.000i q^{64} +(6391.74 + 2072.70i) q^{65} +(3155.98 - 3155.98i) q^{67} +2350.96 q^{68} +(-5519.18 + 5519.18i) q^{70} +(1607.78 - 1607.78i) q^{71} +(22.6121 + 22.6121i) q^{73} -1171.51 q^{74} +(1325.79 + 1325.79i) q^{76} +12352.2i q^{77} +6576.52 q^{79} +(-1799.32 + 1799.32i) q^{80} -3216.64i q^{82} +(5691.45 - 5691.45i) q^{83} +(8261.99 + 8261.99i) q^{85} +(-2011.39 - 2011.39i) q^{86} +4026.98i q^{88} +(-4243.56 - 4243.56i) q^{89} +(3618.20 - 11157.7i) q^{91} -2377.32 q^{92} -5302.58 q^{94} +9318.47i q^{95} +(3532.64 - 3532.64i) q^{97} +(4832.51 + 4832.51i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 18 q^{5} - 42 q^{7} - 96 q^{8} + 18 q^{11} + 90 q^{13} - 168 q^{14} - 384 q^{16} - 366 q^{19} + 144 q^{20} + 72 q^{22} - 12 q^{26} - 336 q^{28} + 6228 q^{29} + 402 q^{31} - 768 q^{32} + 1944 q^{34}+ \cdots + 17076 q^{98}+O(q^{100}) \) 6 * q + 12 * q^2 - 18 * q^5 - 42 * q^7 - 96 * q^8 + 18 * q^11 + 90 * q^13 - 168 * q^14 - 384 * q^16 - 366 * q^19 + 144 * q^20 + 72 * q^22 - 12 * q^26 - 336 * q^28 + 6228 * q^29 + 402 * q^31 - 768 * q^32 + 1944 * q^34 - 3024 * q^35 + 5298 * q^37 + 576 * q^40 + 2430 * q^41 + 144 * q^44 - 1872 * q^46 - 4014 * q^47 - 7908 * q^50 - 768 * q^52 - 6516 * q^53 - 28764 * q^55 + 12456 * q^58 - 7434 * q^59 + 7164 * q^61 + 14598 * q^65 + 5790 * q^67 + 7776 * q^68 - 6048 * q^70 - 15246 * q^71 - 4254 * q^73 + 21192 * q^74 + 2928 * q^76 + 23364 * q^79 + 1152 * q^80 + 38034 * q^83 + 30672 * q^85 - 11160 * q^86 - 4122 * q^89 - 11922 * q^91 - 7488 * q^92 - 16056 * q^94 - 1362 * q^97 + 17076 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more